Facts About Systems of Equation

Identify which method for solving systems is being described by this fact: Equations must be written in slope-intercept form

• Graphing

• Substitution

• Elimination (adding or multiplying)

Identify which method for solving systems is being described by this fact: The intersection point of the two lines is an ordered pair (x, y) and determines the value of the solution to the system of equations.

• Graphing

• Substitution

• Elimination (adding or multiplying)

Identify which method for solving systems is being described by this fact:
If one equation is isolated like y = 2x or x = 7 - 4y then this method should be used.

• Graphing

• Substitution

• Elimination (adding or multiplying)

Identify which method for solving systems is being described by this fact: Use an isolated variable and plug that expression into the second equation in order to solve for the other variable. Plug that value back into the original isolated equation to solve for the second variable.

• Graphing

• Substitution

• Elimination (adding or multiplying)

Two linear equations with the same set of variables

• system of equations

• function

• association

• correlation

Solve the system.

• (2, -2, 3)

• (2, 1, 4)

• (-2, 2, -3)

• No Solution

Solve the system.

• (1, 2, -2)

• (1, -3, -2)

• (-1, 3, 2)

• No Solution

A customer at a store paid $64 for 3 large candles and 4 small candles. At the same store, a second customer paid $4 more than the first customer for 1 large candle and 8 small candles. The price of each large candle is the same, and the price of each small candle is the same. Which system of equations can be used to find the price in dollars of each large candle, x, and each small candle, y?

• 4y = 3x + 64

  8y = x + 68

• 4y = 3x + 64

  8y = x + 60

• 3x + 4y = 64

  x + 8y = 68

• 3x + 4y = 64

  x + 8y = 60

In this system

x+3y=9

4x-2y=-6

we have figured out that x=9-3y, and y=3.

Complete the steps to solve for x:

x=9-3(​ (a)   )

x=9-​ (b)  

x=​ (c)  

The solution to the system is (​ (d)   ,​ (e)   ).

• 3

• 9

• 0

• y

• x

• y=3

• 3y

• -9

• 18

A customer at a store paid $64 for 3 large candles and 4 small candles. At the same store, a second customer paid $4 more than the first customer for 1 large candle and 8 small candles. The price of each large candle is the same, and the price of each small candle is the same. Which system of equations can be used to find the price in dollars of each large candle, x, and each small candle, y?

• 4y = 3x + 64

  8y = x + 68

• 4y = 3x + 64

  8y = x + 60

• 3x + 4y = 64

  x + 8y = 68

• 3x + 4y = 64

  x + 8y = 60